fuel light

The truck will start... when i put the key in the ignition and let the fuel pump pressure up. it will run perfectly for a while and then the fuel light will go on and the truck starts to choke, if i floor the pedal it sometimes kicks back in. now the battery has also died and it is a new battery.

i'm asking for opinons,
the truck is carborated,
what could be wrong? my guess it would be both the alternator and the fuel pump. any suggestions?